Re: It can take 500 years
- From: "Quinn Tyler Jackson" <qtj-query@xxxxxxx>
- Date: Thu, 26 Oct 2006 03:18:50 GMT
Nick replied to me in part with:
For my own part I did find certain aspects of maths difficult, but then
when after my degree and I went hoping to do school teaching I found it
very difficult - for instance about 3 months after I completed my degree I
spent 3 weeks with a class of 10/11 year olds - not on my own - but I was
really on a different planet.
It is only since I have been a long time in the world of work and I have
had to work with people who have real numeracy problems that I really
comprehend the problems that (some of) the kids had.
From an early age, I've struggled with a form of numeric dyslexia called"dyscalculia".* The so-called "simplicity" of simple arithmetic is often
lost on me unless I quadruple check my answers.
Because this is a very noticeable problem, most would "assume" that a
noticeably dyscalculaic person would not have gotten into (or even liked)
mathematics at all.
Dyscalculia doesn't necessarily equate to dysmathematia.
For instance, set and string manipulations might be "simple" to a
dyscalculaic, whereas 12x7 might require using "tricks" to do (and even then
at less speed than those who have that memorized from rote).
A disease with one notation (numbers) might not map to a disease with other
notations, and the notations one uses comfortably have a lot to do with how
well certain problems present themselves per the following quote from
[Whitehead]:
By relieving the brain of all unnecessary work, a good notation sets it free
to concentrate on more advanced problems, and, in effect, increases the
mental power of the race. Before the introduction of the Arabic notation,
multiplication was difficult, and the division even of integers called into
play the highest mathematical faculties. Probably nothing in the modern
world would have more astonished a Greek mathematician than to learn that
.... a large proportion of the population of Western Europe could perform the
operation of division for the largest numbers. This fact would have seemed
to him a sheer impossibility?. Our modern power of easy reckoning with
decimal fractions is the almost miraculous result of the gradual discovery
of a perfect notation. [...] By the aid of symbolism, we can make
transitions in reasoning almost mechanically, by the eye, which otherwise
would call into play the higher faculties of the brain. [...] It is a
profoundly erroneous truism, repeated by all copy-books and by eminent
people when they are making speeches, that we should cultivate the habit of
thinking of what we are doing. The precise opposite is the case.
Civilisation advances by extending the number of important operations which
we can perform without thinking about them. Operations of thought are like
cavalry charges in a battle?they are strictly limited in number, they
require fresh horses, and must only be made at decisive moments.
So is there "simple" or "elementary" math and "advanced" math? I personally
don't think so. There are, however, different weaknesses and strengths
within mathematicians, and different notations bring out those differently.
--
Quinn
http://press.ChevalierEditions.com
* For a good idea of what I'm talking about, see:
http://www.dyscalculia.org/thesis.html
[Whitehead] Alfred North Whitehead, An Introduction to Mathematics, Williams
and Norgate, London, UK, 1911.
.
- References:
- It can take 500 years
- From: Clifford Nelson
- Re: It can take 500 years
- From: Quinn Tyler Jackson
- Re: It can take 500 years
- From: Nick
- It can take 500 years
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